1st Edition

# Multiplicative Differential Equations Volume II

By Svetlin Georgiev, Khaled Zennir Copyright 2023
369 Pages
by Chapman & Hall

369 Pages
by Chapman & Hall

Also available as eBook on:

Multiplicative Differential Equations: Volume II is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second-order multiplicative linear and nonlinear equations are explored. The authors also present first-order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The text is accessible to graduate students and researchers in mathematics, physics, engineering and biology.

Preface

1 Systems Multiplicative Differential Equations
1.1 Systems of Multiplicative Linear Differential Equations
1.2 nth Order MDE
1.3 Multiplicative Homogeneous Systems
1.4 Multiplicative Fundamental Matrix Solutions
1.6 The Method of Variation of Constants
1.7 Systems with Multiplicative Constant Coefficients

2  Qualitative Analysis of Multiplicative Differential Systems
2.1 Periodic Multiplicative Linear Systems
2.2 Asymptotic Behaviour of Solutions I
2.3 Asymptotic Behaviour of Solutions II
2.4 Asymptotic Behaviour of Solutions III
2.5 Asymptotic Behaviour of Solutions IV
2.6 Asymptotic Behaviour of Solutions V
2.7 Asymptotic Behaviour of Solutions VI

3  Stability Theory
3.1 Definition. Examples
3.2 Criteria for Stability
3.3 Uniform Stability
3.4 Stability of Quasi-Multiplicative Linear Systems
3.5 Two-Dimensional Autonomous Systems

4 Multiplicative Linear Boundary Value Problems
4.1 Introduction
4.2 Existence of Solution
4.3 Multiplicative Green Functions

5 Multiplicative Nonlinear MDEs
5.1 Multiplicative Lyapunov Direct Method I
5.2 Multiplicative Lyapunov Direct Method II
5.3 Multiplicative Nonlinear BVPs

6 First Order MPDE
6.1 Classification
6.2 Solvability
6.3 The Cauchy Problem
6.4 The Multiplicative Pfaff Equation
6.5 Some Special Systems